E-resources
-
Navarro, Gonzalo; Sadakane, Kunihiko
ACM transactions on algorithms, 06/2014, Volume: 10, Issue: 3Journal Article
We propose new succinct representations of ordinal trees and match various space/time lower bounds. It is known that any n -node static tree can be represented in 2 n + o ( n ) bits so that a number of operations on the tree can be supported in constant time under the word-RAM model. However, the data structures are complicated and difficult to dynamize. We propose a simple and flexible data structure, called the range min-max tree , that reduces the large number of relevant tree operations considered in the literature to a few primitives that are carried out in constant time on polylog-sized trees. The result is extended to trees of arbitrary size, retaining constant time and reaching 2 n + O ( n /polylog( n )) bits of space. This space is optimal for a core subset of the operations supported and significantly lower than in any previous proposal. For the dynamic case, where insertion/deletion (indels) of nodes is allowed, the existing data structures support a very limited set of operations. Our data structure builds on the range min-max tree to achieve 2 n + O ( n /log n ) bits of space and O (log n ) time for all operations supported in the static scenario, plus indels. We also propose an improved data structure using 2 n + O ( n log log n /log n ) bits and improving the time to the optimal O (log n /log log n ) for most operations. We extend our support to forests, where whole subtrees can be attached to or detached from others, in time O (log 1+ϵ n ) for any ϵ > 0. Such operations had not been considered before. Our techniques are of independent interest. An immediate derivation yields an improved solution to range minimum/maximum queries where consecutive elements differ by ± 1, achieving n + O ( n /polylog( n )) bits of space. A second one stores an array of numbers supporting operations sum and search and limited updates, in optimal time O (log n /log log n ). A third one allows representing dynamic bitmaps and sequences over alphabets of size σ, supporting rank/select and indels, within zero-order entropy bounds and time O (log n log σ/(log log n ) 2 ) for all operations. This time is the optimal O (log n /log log n ) on bitmaps and polylog-sized alphabets. This improves upon the best existing bounds for entropy-bounded storage of dynamic sequences, compressed full-text self-indexes, and compressed-space construction of the Burrows-Wheeler transform.
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.